Endohedral metalofullerenes (EMFs) have emerged as an important class of nanomaterials with vast promise in applications of molecular devices and nanomedicines. This dissertation addresses the EMF research span from synthesis to application, with an emphasis of work on trimetallic nitride template (TNT) EMF and carbide clusterfullerenes (CCFs). As a general introduction, chapter 1 reviews the main literature in TNT EMF studies. Also key works in CCF area are highlighted to show the common feature and uniqueness of this class of EMF in comparison with other EMFs. In the last part of the chapter a list of milestone progress in EMF area has been summarized. Chapter 2 is devoted to the synthetic work on EMFs. Especially, for isotopic modification, the trial and actual EMF syntheses in efforts to introduce 13C, 89Y and 177Lu are described. The next three chapters address the structural characterization of EMFs. Chapter 3 focuses on structural studies of CCFs. With detailed interpretation of 13C NMR and DFT computational results for selected members of the Y2C2@C2n family, the influence of fullerene cage on the size and shape of the yttrium carbide cluster (Y2C2)4+ is investigated. It has also been established that the carbide cluster prefers a linear shape in sufficiently large fullerene cages but adopts a compressed butterfly shape in smaller cages where space is constrained. Chapter 4 presents a systemic examination of dipole moments in TNT EMFs. The first 13C NMR study of M3N@C2(22010)-C78 is achieved on Y3N@C2(22010)-C78. In addition, dipole moments of the M3N@C2n (n=39-44) family are probed by interpretation of chromatographic retention behavior, DFT computational results and single-crystal data. It has been found that TNT EMFs with pentalene motifs exhibit enhanced dipole moments due to the cluster-cage interplay. Chapter 5 provides full characterization of the M2C2@C1(51383)-C84 (M=Y, Gd) molecule, which contains the first example of an asymmetric fullerene cage with fused pentagons. Furthermore, it is suggested that the C1(51383)-C84 cage is capable of a cascade of rearrangements into high symmetry and stable fullerene cages via well-established mechanistic steps, namely, extrusion of C2 units from pentalene or indene motifs and Stone-Wales transformations. As an important intermediate in the formation of high symmetry fullerene cages, the C1(51383)-C84 represents a missing link that implies the "top-down" fullerene formation mechanism. Chapter 6 describes the endeavor to functionalize two exotic EMFs, the room-temperature radical heterometallofullerene Gd2@C79N, and the egg-shaped TNT EMF Gd3N@C84. The reactivity of Gd2@C79N is directly compared to Y2@C79N, Gd3N@C80 and Sc3N@C80 in two reactions and the paramagnetic Gd2@C79N is proven to be very inert toward many known common fullerene cage reactions. Eventually both EMFs have been successfully functionalized via the Bingel reaction, and the derivatives are characterized with HPLC and mass-spectrometry. Chapter 7 compares the effective magnetic moment of Gd3N@C80 and Gd3N@C84, together with the previously reported Gd@C82. The magnetic moment has a second-order contribution to the T1 relaxivity and thereby is an important factor to evaluate an EMF's value in application as MRI contrast agents. Furthermore the influence of cluster motion to magnetic behavior in TNT EMF is discussed. / Ph. D.

Quantum information processing (QIP), which inherently utilizes quantum mechanical phenomena to perform information processing, may outperform its classical counterpart at certain tasks. As one of the physical implementations of QIP, the electron-spin based architecture has recently attracted great interests. Endohedral fullerenes with unpaired electrons, such as N@C₆₀, are promising candidates to embody the qubits because of their long spin decoherence time. This thesis addresses several fundamental aspects of the strategy of engineering the N@C₆₀ molecules for applications in QIP. Chemical functionalization of N@C₆₀ is investigated and several different derivatives of N@C₆₀ are synthesized. These N@C₆₀ derivatives exhibit different stability when they are exposed to ambient light in a degassed solution. The cyclopropane derivative of N@C60 shows comparable stability to pristine N@C₆₀, whereas the pyrrolidine derivatives demonstrate much lower stability. To elucidate the effect of the functional groups on the stability, an escape mechanism of the encapsulated nitrogen atom is proposed based on DFT calculations. The escape of nitrogen is facilitated by a 6-membered ring formed in the decomposition of the pyrrolidine derivatives of N@C₆₀. In contrast, the 4-membered ring formed in the cyclopropane derivative of N@C₆₀ prohibits such an escape through the addends. Two N@C₆₀-porphyrin dyads are synthesized. The dyad with free base porphyrin exhibits typical zero-field splitting (ZFS) features due to functionalization in the solid-state electron spin resonance (ESR) spectrum. However, the nitrogen ESR signal in the second dyad of N@C₆₀ and copper porphyrin is completely suppressed at a wide range of sample concentrations. The dipolar coupling between the copper spin and the nitrogen spins is calculated to be 27.0 MHz. To prove the presence of the encapsulated nitrogen atom in the second dyad, demetallation of the copper porphyrin moiety is carried out. The recovery of approximately 82% of the signal intensity confirms that the dipolar coupling suppresses the ESR signal of N@C₆₀. To prepare ordered structure of N@C₆₀, the nematic matrix MBBA is employed to align the pyrrolidine derivatives of N@C₆₀. Orientations of these derivatives are investigated through simulation of their ESR spectra. The derivatives with a –CH3 or phenyl group derived straightforward from the N-substituent of the pyrrolidine ring are preferentially oriented based on their powder-like ESR spectra in the MBBA matrix. An angle of about is also found between the directors of fullerene derivatives and MBBA. In contrast, the derivatives with a –CH₂ group inserted between the phenyl group and the pyrrolidine ring are nearly randomly distributed in MBBA. These results illustrate the applicability of liquid crystal as a matrix to align N@C₆₀ derivatives for QIP applications.

Cette thèse avait pour premier objectif de comprendre les mécanismes d'auto-organisation entre nanoparticules de ZnO. Synthétisées via une technique physique combinant ablation laser et détente supersonique (la LECBD), les nanoparticules obtenues sont stoechiométriques, cristallisées et sans ligand. Grâce à la DRX et HRTEM, nous avons pu identifier la nature du mécanisme régissant le collage orienté des nanoparticules. Son impact sur la luminescence de couches minces de ZnO est de première importance pour des applications opto-électroniques. La microscopie confocale nous a permis de caractériser finement les spectres optiques de films nanostructurés. Une méthode originale combinant STEM et cathodoluminescence a permis de révéler une hétérogénéité nanométrique de la luminescence issue du collage orienté. Par ailleurs, des phénomènes fondamentaux tels que le blinking, ou bleaching pour une nanoparticule unique de ZnO ne sont pas connus. La LECBD permet d'obtenir des nanoparticules isolées et triées en masse. Nous avons ainsi pu observer la luminescence d'une collection de 50 nanoparticules sous faisceau (état de l'art), donnant accès aux paramètres intrinsèques de la luminescence d'une particule unique. A ce jour, le dopage de type p par substitution reste un verrou technologique dans ZnO freinant le développement d'applications optoélectroniques. Un dernier objectif a donc été d'explorer numériquement les possibilités d'un autre type de dopage dans ZnO à savoir le dopage endohédral. Nous avons montré que le dopage de type p était possible dans la sodalite, une structure cage hypothétique pour ZnO, ce qui ouvre la voie à de nouveaux champs d'investigation dans ce domaine / The understanding of the self-organization mechanisms between ZnO nanoparticles was a first objective of this thesis. Synthesized via a physical technique combining a laser ablation and a supersonic expansion (LECBD), nanoparticles are stoichiometric, crystallized and ligand-free. Thanks to XRD and HRTEM, we could identify the nature of the mechanism governing the oriented attachment between nanoparticles, still under debate in the literature. Its impact on the luminescence of ZnO thin films is of primary importance for opto-electronic applications. Confocal microscopy allowed us to characterize accurately the optical spectra of nanostructured films. A novel method combining STEM and cathodoluminescence revealed a nanometer scaled heterogeneity of luminescence from oriented attached structures. Moreover, fundamental phenomena such as blinking or bleaching for a single ZnO nanoparticle are not yet known. Thanks to LECBD it is possible to synthesize isolated and weight selected nanoparticles. We were able to observe the luminescence of a collection of 50 nanoparticles under the beam (state of the art), giving us access to the intrinsic parameters of the luminescence of a single particle. On the other hand and up to date, the p-type doping by substitution remains a technological barrier in ZnO constraining the development of opto-electronic applications. Thus, as a final objective we explored numerically the possibilities of another scheme of doping in ZnO namely the endohedral doping. We have shown that the p-type doping was possible in the sodalite, a hypothetical cage structure for ZnO, which opens the way to new fields of investigation in this area

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.

Quantum information processing (QIP) has the potential to reduce the complexity of many classically ‘hard’ computational problems. To implement quantum information algorithms, a suitable physical quantum computer architecture must be identified. One approach is to store quantum information in the electron spins of an array of paramagnetic N@C₆₀ endohedral fullerene molecules, using the electron-electron dipolar interaction to permit the formation of the entangled quantum states needed to implement QIP. This thesis explores two different chemical methods to create two-spin centre arrays that contain N@C₆₀. The first method uses a double 2,3 dipolar cycloaddition reaction to a dibenzaldehyde-terminated oligo-p-phenylene polyethynylene (OPE) unit , to create an (S_3/2, S_3/2) N@C₆₀-N@C₆₀ dimer with a fixed spin centre separation of 2.7 nm. The second approach is via a self-assembly scheme in which a Lewis base functionalised N@C₆₀ molecule coordinates to an antiferromagnetic metallic ring magnet to form a (S_3/2, S_3/2) two-spin centre N@C₆₀-Cr₇Ni system with an inter-spin separation of 1.4 nm. In both systems, a significant perturbation of the electron spin transition energies is observed using CW ESR, this perturbation is shown to be well accounted for by the inclusion of an electron-electron dipolar coupling term in the electron spin Hamiltonians. To create entanglement in an ensemble of two-spin centre molecules, the dipolar coupling interaction must lie within a narrow distribution. To achieve this not only the separation but also the orientation of the inter-spin axis with respect to the applied magnetic field must be controlled for which a method of macroscopic alignment is required. The potential of using a uniaxially drawn liquid crystal elastomer to exert uniaxial order on fullerene dimers is tested, finding that the degree of alignment is insufficient, possibly a result of the propensity for the fullerene molecules to phase separate from the elastomer. This phase separation is shown to restrict N@C₆₀ phase coherence lifetime to 1.4 µs at 40 K due to instantaneous spin diffusion. The electron spin environment of both N@C₆₀ and an N@C₆₀-C₆₀ dimer in a polymer matrix is examined using polystyrene as the host matrix. By deuteration of the polystyrene matrix, a maximum phase coherence lifetimes of 48 µs and 21 µs are measured for the N@C₆₀ and N@C₆₀-C₆₀ dimer, respectively. The concept of reading out the electron spin state of N@C₆₀ molecules by coupling it to a spin system that can be probed using optically detected magnetic resonance (ODMR) such as an NV- centre has been previously suggested. To this end, the photostability of N@C₆₀ under 637 nm laser illumination has been examined in solution. The effect of the presence of an atmospheric concentration of oxygen is striking, affording a 57-fold retardation in the photodecomposition of N@C₆₀ compared to a degassed solution. When ambient oxygen is present, the average number of excitations that are required to cause decomposition is ≈60000. Finally, for future UV photophysics experiments involving N@C₆₀, the best solvent to use was found to be decalin, finding that it significantly slowed decomposition of N@C₆₀ in both ambient and degassed solutions. The conclusions of this work make a significant contribution to the field of QIP with N@C₆₀, showing that there is a bright future for N@C₆₀.

This work describes theoretical studies on molecular and electronic structures of lanthanide-based single-molecule magnets focusing on their magnetic properties. In this work, two main problems are covered: the structural ordering of endohedral fullerenes in different supramolecular arrangements, and the magnetic anisotropy of lanthanides in different charge coordinations. The basic methodes used in this work are density functional theory and multiconfigurational self-consistent field.:CHAPTER 1. THEORETICAL FOUNDATIONS OF RARE-EARTH MAGNETISM 12 1.1. Single-molecule magnetism and 4f-elements 14 1.1.1. Electronic structure of 4f-elements 16 1.1.2. LS-coupling scheme 19 1.1.3. Parameterization of the Crystal-Field splitting effect. 20 1.1.4. Zeeman splitting for a free ion 24 1.1.5. Spin Hamiltonian and pseudospin approximation 24 1.1.6. Kramers theorem 25 1.1.7. Weak and strong molecular interactions. 26 1.2. Computational methods in application to Ln-based SMMs 27 1.2.1. Density functional theory (DFT). 28 1.2.2. Multiconfigurational methods in quantum chemistry 33 1.3. Role of molecular structure in single-molecular magnetism 41 1.3.1. Complexes of SMMs with organic molecules 45 1.3.2. SMMs deposited on surfaces 46 CHAPTER 2. STRUCTURAL ORDERING IN COCRYSTALS OF EMFs AND Ni(OEP) 49 2.1. Ordering in endohedral metallofullerenes 49 2.2. Modeling details 51 2.3. Conformer analysis 54 2.4. Electrostatic potential 58 CHAPTER 3. ISOMERISM OF Dy2ScN@C80 DEPOSITED ON SURFACES 61 3.1. Modeling details 62 3.2. Cluster conformation analysis 69 3.3. Charge density analysis 75 CHAPTER 4. Ho|MgO AS A SINGLE-ATOMIC MAGNET. FV-MAGNETISM. 80 4.1. DFT description of Ln|MgO 85 4.2. Ho|MgO system: ab initio calculations 92 4.3. Magnetic properties of lanthanides with FV magnetism 99 4.4. Generalized ligand field and spin Hamiltonians for FV systems. 101 CHAPTER 5. FV-MAGNETISM IN [Ln2+] METALLOCENE COMPLEXES 107 5.1. TbII(CpiPr5)2 DFT-model 108 5.2. FV-interaction in terms of ab initio multiconfigurational approach 113 5.3. Point-charge model 115

In this thesis, a series of computational studies based on density functional theory (DFT) and density functional tight-binding (DFTB) is presented to deeply understand experimental results on the synthesis of endohedral fullerenes and graphene/iron hybrids at atomic level. In the first part, a simple and efficient model is proposed to evaluate the strain experienced by clusters encapsulated in endohedral metallofullerenes (EMFs). Calculations for the sole cluster, either in the neutral or the charged state, cannot be used for this goal. However, when the effect of the carbon cage is mimicked by small organic π-systems (such as pentalene and sumanene), the cluster has sufficient freedom to adopt the optimal configuration, and therefore the energetic characteristics of the EMF-induced distortion of the cluster can be evaluated. Both nitride and sulfide clusters were found to be rather flexible. Hence, they can be encapsulated in carbon cages of different size and shape. For carbide M2C2 cluster the situation is more complex. The optimized cluster can adopt either butterfly or linear shapes, and these configurations have substantially different metal-metal distance. Whereas for Sc2C2 both structures are isoenergetic, linear form of the Y2C2 cluster is substantially less stable than the butterfly-shaped configuration. These results show that phenomenon of the “nanoscale fullerene compression” once proposed by Zhang et al. (J. AM. CHEM. SOC. (2012),134(20)) should be “nanoscale fullerene stretching”. Finally, the results also reveal that both Ti2S and Ti2C2 cluster are strained in corresponding EMF molecules, but the origin of the strain is opposite: C78-D3h(5) cage imposes too long Ti···Ti distance for the sulfide cluster and too short distance for the carbide cluster. In the second part of the thesis, possible fullerene geometries and electronic structures have been explored theoretically for the species detected in mass spectra of the Sc-EMF extract synthesized using CH4 as a reactive gas. Two most promising candidates, namely Sc4C@C80-Ih(7) and Sc4C3@C80-Ih(7), have been identified and further studied at the DFT level. For Sc4C@C80, the tetrahedral Sc4 cluster with the central μ4-C atom was found to be 10 kJ/mol more stable than the square cluster. For Sc4C3@C80, the calculation showed that the most stable is the Sc4C3 cluster in which the triangular C3 moiety is η3- and η2-coordinated to Sc atoms. Whereas Sc4C@C80 has rather small HOMO-LUMO gap and low ionization potential, the HOMO-LUMO gap of Sc4C3@C80 is substantially higher and exceeds that of Sc4C2@C80. In the third part, computational studies of structures and reactivity are described for a new type of EMFs with a heptagon that has been produced in the arc-discharge synthesis. DFT computations predict that LaSc2N@Cs(hept)-C80 is more stable than LaSc2N@D5h-C80, so the former should be synthesized in much higher yield than observed. This disagreement may be ascribed to the kinetic factors rather than thermodynamic stability. Because of prospective applications of this EMFs by introducing functional groups, the influence of the heptagon on the chemical properties have been further evaluated. Thermodynamically and kinetically preferred reaction sites are studied computationally for Prato and Bingel-Hirsch cycloaddition reactions. In both types of reactions the heptagon is not affected, and chemical reactivity is determined by the adjacent pentalene units. Thermodynamically controlled Prato addition is predicted to proceed regioselectively across the pentagon/pentagon edges, whereas the most reactive sites in kinetically-controlled Bingel-Hirsch reaction are the carbon atoms next to the pentagon/pentagon edge. Fourth, although various EMFs have been successfully synthesized and characterized, the formation mechanism is still not known in details, and hence control of the synthesis products is rather poor. Therefore, EMF self-assembly process in Sc/carbon vapor in the presence and absence of cooling gas (helium) and reactive gas (NH3 and CH4) is systematically investigated using quantum chemical molecular dynamics (QM/MD) simulations based on the DFTB potentials. The cooling gas effect is that the presence of He atoms accelerates formation of pentagons and hexagons and reduces the size of formed carbon cages in comparison to the analogous He-free simulations. As a result, the Sc/C/He system yields a large number of successful trajectories (i.e. leading to the Sc-EMFs) with more realistic cage-size distribution than the Sc/C system. Encapsulation of Sc atoms within the carbon cage was found to proceed via two parallel mechanisms. The main mechanism involves nucleation of the several hexagons and pentagons with Sc atoms already at the early stages of the carbon vapor condensation. In such proto-cages, both Sc–C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at high temperatures. Further growth of the carbon cage results in encapsulation of one or two Sc atoms within the forming fullerene. Another encapsulation mechanism is observed in rare cases. In this process, the closed cage is formed with Sc being a part of the carbon network, i.e. being bonded by three or four Sc–C σ-bonds. However, such intermediates are found to be unstable, and transform into the endohedral fullerenes within few picoseconds of annealing. In perfect agreement with experimental studies, extension of the simulation to Fe and Ti showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3). The role of “reactive gas” in the EMF synthesis is revealed in dedicated simulations of the fullerene formation in the presence of several molecules of CH4 or NH3. When concentration of reactive gas is high, carbon vapor tends to form graphene flakes or other carbon species terminated by hydrogen atoms, whereas the yield of empty fullerenes is very low. Conversely, with additional metal atoms (Sc) and the same number of NH3 molecules, the yield of fullerenes constantly increase from 5 to 65% which is ascribed to the catalytic activity of metal atoms in the nucleation of carbon cages already at early stage. Moreover, due to the presence of hydrogen atoms from the reactive gas, the carbon cage formation requires much longer time, which provides sufficient reaction time to encapsulate 3 or 4 Sc atoms within one cage. It explains preferential formation of clusterfullerenes in experiments with reactive gas. At the same time, monometallofullerenes and dimetallofullerenes are the main products in absence of reactive gas. We also provide possible growth mechanisms of carbide and cyano-clusterfullerenes in details to elucidate how the intracluster goes into the cage. A possible growth mechanism of nitride clusterfullerenes has been proposed based on DFT results. In the last part, a free-standing crystalline single-atom thick layer of Fe has been studied theoretically. By investigating the energy difference, ΔE, between a suspended Fe monolayer and a nanoparticle using the equivalent number of Fe atoms, one can estimate that the largest stable membrane should be ca. 12 atoms wide or 3 × 3 nm2 which is in excellent agreement with the experimental observation. Otherwise, the possibility of C, O, N atoms embedded into the Fe membrane can been fully excluded by DFTB and DFT simulations, which agrees with electron energy loss spectroscopy (EELS) measurement. A significantly enhanced magnetic moment for single atom thick Fe membranes (3.08 μB) is predicted by DFT as compared to the bulk BCC Fe (2.1 μB), which originates from the 2D nature of the Fe membrane since the dz2 orbital is out-of-plane while the dxy orbital is in-plane.